where \(\kappa >0\)  is again the coupling strength, the Hermitian matrix \(H_i\)  is the Hamiltonian of \(U_i\) , and \(\dagger \)  denotes the Hermitian conjugate. It can be checked that the Kuramoto model is the \(U(1)\)  case of the Lohe model (REF ), and the Lohe model (REF ) is in turn the case \(G=U(d)\) , \(\phi (U)=\frac{1}{2} (U-U^\dagger )\)  of the generalized Kuramoto–Lohe model. Lohe [1]} numerically observed Theorem REF  for the \(U(2)\)  model, and the author and Ha [2]} gave a rigorous proof of Theorem REF  for all unitary groups \(U(d)\) .
